Radar system with modified orthogonal linear antenna subarrays

ABSTRACT

This document describes techniques and systems of a radar system with modified orthogonal linear antenna subarrays and an angle-finding module. The described radar system includes a first one-dimensional (1D) (e.g., linear) subarray; a second 1D subarray positioned orthogonal to the first 1D subarray; and a two-dimensional (2D) subarray. Using electromagnetic energy received by the first 1D subarray and the second 2D subarray, azimuth angles and elevation angles associated with one or more objects can be determined. The radar system associates, using electromagnetic energy received by the 2D subarray, pairs of an azimuth angle and an elevation angle to the respective objects. In this way, the described systems and techniques can reduce the number of antenna elements while maintaining the angular resolution of a rectangular 2D array with similar aperture sizing.

BACKGROUND

Radar systems use antennas to transmit and receive electromagnetic (EM)signals for detecting and tracking objects. In automotive applications,radar antennas can include a two-dimensional (2D) array of elements tomeasure an azimuth angle and elevation angle associated with theobjects. The resolution of these azimuth and elevation angles isgenerally proportional to the aperture size of the array. Realizing alarge aperture with a 2D array may require many antenna elements, whichincreases cost. It is desirable to maintain the angular resolution ofradar systems without adding additional antenna elements and withoutincreasing cost.

SUMMARY

This document describes techniques and systems of a radar system withmodified orthogonal linear antenna subarrays. Even with far fewerantenna elements than a traditional radar system, these modifiedsubarrays enable an example radar system to have comparable angularresolution at a lower cost and lower complexity level. For example, aradar system includes a processor and an antenna that can receiveelectromagnetic energy reflected by one or more objects. The antennaincludes a first one-dimensional (1D) (e.g., linear) subarray, a second1D subarray, and a two-dimensional (2D) subarray. The second 1D subarrayis positioned orthogonal to the first 1D subarray. The 2D subarrayincludes at least four antenna elements not encompassed by the first 1Dsubarray or the second 1D subarray. The processor can determine, usingelectromagnetic energy received by the first 1D subarray and the second1D subarray, first and second angles associated with the one or moreobjects. The processor then associates, using electromagnetic energyreceived by the 2D subarray, the first angles and the second angles withrespective objects of the one or more objects.

This document also describes methods performed by the above-summarizedsystem and other configurations of the radar system set forth herein, aswell as means for performing these methods.

This Summary introduces simplified concepts related to a radar systemwith modified orthogonal linear antenna subarrays, which are furtherdescribed below in the Detailed Description and Drawings. This Summaryis not intended to identify essential features of the claimed subjectmatter, nor is it intended for use in determining the scope of theclaimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

The details of one or more aspects of a radar system with modifiedorthogonal linear antenna subarrays are described in this document withreference to the following figures. The same numbers are often usedthroughout the drawings to reference like features and components:

FIG. 1 illustrates an example environment in which a radar system withmodified orthogonal linear antenna subarrays can be implemented;

FIGS. 2A-2F illustrate example antennas with modified orthogonal linearantenna subarrays;

FIG. 3 illustrates an example flow diagram of a radar system withmodified orthogonal linear antenna subarrays;

FIG. 4 illustrates an example flow diagram of an angle-finding module toassociate azimuth angles and elevation angles to respective objects; and

FIG. 5 illustrates an example method of a radar system with modifiedorthogonal linear antenna subarrays and an angle-finding module.

DETAILED DESCRIPTION

Overview

Radar systems are an important sensing technology that some automotivesystems rely on to acquire information about the surroundingenvironment. Radar systems generally include at least two antennas totransmit and receive EM radiation. Some radar systems include a receiveantenna with a two-dimensional (2D) planar array of antenna elements tomeasure both the azimuth angle and the elevation angle associated withobjects. A large aperture in the azimuth direction and the elevationdirection of the receive antenna can increase the number of antennaelements and the cost of the radar system.

Some radar systems include a receive antenna with a two-dimensional (2D)planar array of antenna elements to measure both the azimuth angle andthe elevation angle of objects. In radar systems with a 2D planarantenna array, the radar system can estimate the angular position ofobjects using digital beamforming. In digital beamforming, the radarsystem characterizes the angular information of the object by analyzingthe relative phase across the antenna elements of the 2D planar arrayusing a 2D fast Fourier transform (FFT). The angular resolution of suchradar systems generally depends on the aperture size of the 2D planararray. A larger aperture size can improve the angular resolution butrequires additional antenna elements and increased costs.

Other radar systems include a receive antenna with two orthogonal lineararrays of antenna elements to occupy the azimuth direction and elevationdirection of the antenna array. The radar system can use the azimuthlinear array and the elevation linear array to measure the azimuth andelevation angles of objects, respectively. These radar systems usematching algorithms to associate the azimuth angle and elevation anglefor each object. Although such systems generally include fewer antennaelements than planar 2D arrays, the angle finding for these systems istoo complicated for many applications, including automotiveapplications. In particular, the radar systems use cross-correlationmatrix-based methods that require multiple data snapshots from thelinear array to associate a single set of angle measurements. Becauseautomotive radar systems generate a single snapshot while a vehiclemoves, such methods are inapplicable to automotive applications.

Some other radar systems with orthogonal linear arrays usefrequency-modulated continuous-wave signals. These radar systems use abeam-matching method to associate an azimuth angle and an elevationangle. The beam-matching method converts the beam-matching problem to animage-patch matching problem in a range-Doppler domain. This method,however, can only work for applications where only a single objectexists in any given range-Doppler bin. If two objects are in the samerange-Doppler bin, these radar systems are generally unable toaccurately pair the azimuth angle and elevation angle for the respectiveobjects. This inability to accurately associate the azimuth angles andelevation angles restricts these radar systems from automotive radarapplications in which multiple objects can often exist in the samerange-Doppler bin.

In contrast, this document describes techniques and systems to provide areceive antenna with orthogonal one-dimensional (1D) subarrays and a 2Dsubarray, for supporting angle finding features. For example, a radarsystem can include an antenna array with a first 1D subarray, a second1D subarray, and a 2D subarray. The second 1D subarray is positionedorthogonal to the first 1D subarray. The 2D subarray includes at leastfour antenna elements not encompassed by the first or second 1Dsubarrays. In this way, the described systems and techniques can reducethe number of antenna elements while preserving the angular resolutionthat can otherwise be achieved using a rectangular 2D array with similaraperture sizing.

The radar system determines, using EM energy received by the first andsecond 1D subarrays, first and second angles, respectively, associatedwith one or more nearby objects. The radar system can then associate,using EM energy received by the 2D subarray, the first and second angleswith respective objects of the one or more objects. In this way, thecomputational complexity for the described radar system to associate thefirst angles and second angles to respective objects is similar to thecomputational complexity for a conventional radar system withconventional 2D planar arrays. The described angle-finding technique canbe applied to various configurations of the described orthogonal 1Dsubarrays with a 2D subarray.

This is just one example of the described techniques and systems of aradar antenna with modified orthogonal linear arrays. This documentdescribes other examples and implementations.

Operating Environment

FIG. 1 illustrates an example environment 100 in which a radar system102 with modified orthogonal linear antenna subarrays can beimplemented. In the depicted environment 100, the radar system 102 ismounted to, or integrated within, a vehicle 104. The radar system 102can detect one or more objects 106 that are in the vicinity of thevehicle 104. Although illustrated as a car, the vehicle 104 canrepresent other types of motorized vehicles (e.g., a motorcycle, a bus,a tractor, a semi-trailer truck), non-motorized vehicles (e.g., abicycle), railed vehicles (e.g., a train), watercraft (e.g., a boat),aircraft (e.g., an airplane), or spacecraft (e.g., satellite). Ingeneral, manufacturers can mount the radar system 102 to any movingplatform, including moving machinery or robotic equipment.

In the depicted implementation, the radar system 102 is mounted on thefront of the vehicle 104 and illuminates the object 106. The radarsystem 102 can detect the object 106 from any exterior surface of thevehicle 104. For example, vehicle manufacturers can integrate the radarsystem 102 into a bumper, side mirror, headlights, rear lights, or anyother interior or exterior location where the object 106 requiresdetection. In some cases, the vehicle 104 includes multiple radarsystems 102, such as a first radar system 102 and a second radar system102, that provide a larger field-of-view. In general, vehiclemanufacturers can design the locations of the one or more radar systems102 to provide a particular field-of-view that encompasses a region ofinterest. Example fields-of-view include a 360-degree field-of-view, oneor more 180-degree fields-of-view, one or more 90-degree fields-of-view,and so forth, which can overlap or be combined into a field-of-view of aparticular size.

The object 106 is composed of one or more materials that reflect radarsignals. Depending on the application, the object 106 can represent atarget of interest. In some cases, the object 106 can be a moving object(e.g., another vehicle) or a stationary object (e.g., a roadside sign).

The radar system 102 emits EM radiation by transmitting EM signals orwaveforms via antenna elements. In the environment 100, the radar system102 can detect and track the object 106 by transmitting and receivingone or more radar signals. For example, the radar system 102 cantransmit EM signals between 100 and 400 gigahertz (GHz), between 4 and100 GHz, or between approximately 70 and 80 GHz.

The radar system 102 can include a transmitter 120 and at least oneantenna 124 to transmit EM signals. The radar system 102 can alsoinclude a receiver 122 and the at least one antenna 124 to receivereflected versions of the EM signals. The transmitter 120 includes oneor more components for emitting the EM signals. The receiver 122includes one or more components for detecting the reflected EM signals.The transmitter 120 and the receiver 122 can be incorporated together onthe same integrated circuit (e.g., a transceiver integrated circuit) orseparately on different integrated circuits.

The radar system 102 also includes one or more processors 126 (e.g., anenergy processing unit) and computer-readable storage media (CRM) 128.The processor 126 can be a microprocessor or a system-on-chip. Theprocessor 126 can execute instructions stored in the CRM 128. Forexample, the processor 126 can process EM energy received by the antenna124 and determine, using an angle-finding module 130, a location of theobject 106 relative to the radar system 102. The processor 126 can alsogenerate radar data for at least one automotive system. For example, theprocessor 126 can control, based on processed EM energy from the antenna124, an autonomous or semi-autonomous driving system of the vehicle 104.

The angle-finding module 130 obtains EM energy received by the antenna124 and determines azimuth angles and elevation angles associated withthe object 106. The angle-finding module 130 can be implemented asinstructions in the CRM 128, hardware, software, or a combinationthereof that is executed by the processor 126.

The radar system 102 can determine a distance to the object 106 based onthe time it takes for the EM signals to travel from the radar system 102to the object 106, and from the object 106 back to the radar system 102.The radar system 102 can also determine, using the angle-finding module130, a location of the object 106 in terms of an azimuth angle 116 andan elevation angle 118 based on the direction of a maximum-amplitudeecho signal received by the radar system 102.

As an example, FIG. 1 illustrates the vehicle 104 traveling on a road108. The radar system 102 detects the object 106 in front of the vehicle104. The radar system 102 can define a coordinate system with an x-axis110 (e.g., in a forward direction along the road 108), a y-axis 112(e.g., perpendicular to the x-axis 110 and along a surface of the road108), and a z-axis 114 (e.g., perpendicular to the surface of the road108). The radar system 102 can locate the object 106 in terms of theazimuth angle 116 and the elevation angle 118. The azimuth angle 116 canrepresent a horizontal angle from the x-axis 110 to the object 106. Theelevation angle 118 can represent a vertical angle from the surface ofthe road 108 (e.g., a plane defined by the x-axis 110 and the y-axis112) to the object 106.

The vehicle 104 can also include at least one automotive system thatrelies on data from the radar system 102, such as a driver-assistancesystem, an autonomous-driving system, or a semi-autonomous-drivingsystem. The radar system 102 can include an interface to an automotivesystem that relies on the data. For example, the processor 126 outputs,via the interface, a signal based on EM energy received by the antenna124.

Generally, the automotive systems use radar data provided by the radarsystem 102 to perform a function. For example, the driver-assistancesystem can provide blind-spot monitoring and generate an alert thatindicates a potential collision with the object 106 that is detected bythe radar system 102. In such an implementation, the radar data from theradar system 102 indicates when it is safe or unsafe to change lanes.The autonomous-driving system may move the vehicle 104 to a particularlocation on the road 108 while avoiding collisions with the object 106detected by the radar system 102. The radar data provided by the radarsystem 102 can provide information about a distance to and the locationof the object 106 to enable the autonomous-driving system to performemergency braking, perform a lane change, or adjust the speed of thevehicle 104.

FIGS. 2A-2F illustrate example antennas 200 with modified orthogonallinear antenna subarrays. The antennas 200 are examples of the antenna124 of the radar system 102 in FIG. 1 , with similar components. Theantennas 200 include a first 1D subarray 204 (e.g., an azimuthsubarray), a second 1D subarray 206 (e.g., an elevation subarray), and a2D subarray 208 on a printed circuit board (PCB) 202. In operation, theantennas 200 can receive EM energy reflected by one or more objects 106.

In the depicted implementations, the first antenna subarray 204 ispositioned in an azimuth direction and is hereinafter referred to as theazimuth subarray 204. The second antenna subarray 206 is positioned inan elevation direction and is hereinafter referred to as the elevationsubarray 206. The elevation subarray 206 is positioned orthogonal to theazimuth subarray 204. The azimuth subarray 204 and the elevationsubarray 206 can be linear subarrays.

The azimuth subarray 204 and the elevation subarray 206 can be arrangedin an approximately L shape, as illustrated in FIGS. 2A, 2E, and 2F; anapproximately T shape, as illustrated in FIGS. 2B and 2C; or anapproximately cross shape, as illustrated in FIG. 2D. Radar designers orradar manufacturers can arrange the antenna elements of the azimuthsubarray 204 and the elevation subarray 206 in other approximate shapeswith the elevation subarray 206 positioned orthogonal to the azimuth subarray 204.

The antenna elements 210 of the 2D subarray 208 can be arranged in anapproximately rectangular shape, as illustrated in FIGS. 2A-2E. Theseantenna elements 210 can be positioned close to (e.g., as illustrated inFIGS. 2A and 2B), overlapping with (e.g., as illustrated in FIGS. 2C and2D), or separated from (e.g., as illustrated in FIGS. 2E and 2F) theazimuth subarray 204 and/or the elevation subarray 206. The antennaelements 210 of the 2D subarray 208 can also be arranged in atwo-dimensional sparse array, as illustrated in FIG. 2F. The specificarrangement of the azimuth subarray 204, the elevation subarray 206, andthe 2D subarray 208 can be chosen based on the position and arrangementof other components in the radar system 102.

The azimuth subarray 204, the elevation subarray 206, and the 2Dsubarray 208 include multiple antenna elements 210. The azimuth subarray204 can include M antenna elements 210. The elevation subarray 206 caninclude N antenna elements 210, where Nis equal or not equal to M. The2D subarray 208 can include P antenna elements 210 not encompassed bythe azimuth subarray 204 or the elevation subarray 206. In automotiveapplications, the number of antenna elements 210 in the 2D subarray 208can be greater than an anticipated maximum number of objects 106 to bedetected by the radar system 102. The number of antenna elements 210 inthe 2D subarray, P, is generally less than the product of M and N (e.g.,P<<M×N). In some implementations, P is less than half of the product ofM and N

$( {{e.g.},{P < \frac{M \times N}{2}}} ).$The total number of antenna elements 210 in the antenna 200 generallyequals M+N+P−1, where one antenna element 210 is shared by the azimuthsubarray 204 and the elevation subarray 206. The number of antennaelements 210 in the antenna 200 (e.g., M+N+P−1) is generally much lessthan the number of antenna elements 210 in a rectangular array (e.g.,M×N) with the same aperture sizing.

In the depicted implementations, the azimuth subarray 204 includes nineantenna elements 210, the elevation subarray 206 includes eight antennaelements 210, and the 2D subarray 208 includes six antenna elements 210not encompassed by the azimuth subarray 204 or the elevation subarray206. The antennas 200 include 22 antenna elements 210, much less than 72antenna elements included in a rectangular array with the same aperturesizing. In other implementations, the azimuth subarray 204, theelevation subarray 206, or the 2D subarray 208 can include fewer oradditional antenna elements 210. The 2D subarray 208 generally includesat least four antenna elements 210 not encompassed by the azimuthsubarray 204 or the elevation subarray 206.

The antenna elements 210 in the azimuth subarray 204 and the 2D subarray208 are separated by an azimuth distance 212, d_(AZ). Similarly, theantenna elements 210 in the elevation subarray 204 and the 2D subarray208 are separated by an elevation distance 214, d_(EL). As describedwith respect to FIG. 5 , the angle-finding module 130 uses the azimuthdistance 212 and the elevation distance 214 to associate an elevationangle to an azimuth angle for the object 106.

The azimuth subarray 204, the elevation subarray 206, and the 2Dsubarray 208 can be planar arrays that provide high gain and low loss.Planar arrays are well-suited for vehicle integration due to their smallsize. For example, the antenna elements 210 can be slots etched orotherwise formed in a plating material of one surface of the PCB 202 fora substrate-integrated waveguide (SIW) antenna. The antenna elements 210can also be part of an aperture antenna, a microstrip antenna, or adipole antenna. For example, the azimuth subarray 204, the elevationsubarray 206, and the 2D subarray 208 can include subarrays of patchelements (e.g., microstrip patch antenna subarrays) or dipole elements.

FIG. 3 illustrates an example flow diagram 300 of the radar system 102with modified orthogonal linear antenna subarrays and the angle-findingmodule 130. The radar system 102 of FIG. 3 can, for example, be theradar system 102 of FIG. 1 . The radar system 102 includes two 1Dsubarrays positioned orthogonal to one another, along with a 2Dsubarray. In the depicted implementation, the radar system 102 includesthe azimuth subarray 204, the elevation subarray 206, and the 2Dsubarray of antenna 200, which can be arranged in a variety ofpositions, including the arrangements illustrated in FIGS. 2A-2F.

At 304, the angle-finding module 130 obtains EM energy 302 received bythe azimuth subarray 204 and determines azimuth angles 306 associatedwith one or more azimuth objects. The azimuth angles 306 include θ₁, θ₂,. . . , θ_(N) _(Az) , where N_(AZ) represents the number of azimuthobjects.

At 310, the angle-finding module 130 obtains EM energy 308 received bythe elevation subarray 206 and determines elevation angles 312associated with one or more elevation objects. The elevation angles 312include (φ₁, (φ₂, . . . , (φ_(N) _(EL) , where N_(EL) represents thenumber of elevation objects. Because two or more of the objects 106 canhave the same azimuth angles 306 and/or the same elevation angles 312,the number of elevation objects, N_(EL), can be different than thenumber of azimuth objects, N_(AZ). For example, the radar system 102 candetect three objects 106 (e.g., three vehicles in front of the vehicle104), each of which can have the same elevation angle 312 relative tothe radar system 102 but different azimuth angles 306. As a result, theangle-finding module 130 would identify one elevation object but threeazimuth objects.

The angle-finding module 130 can use various angle-finding functions todetermine the azimuth angles 306 and the elevation angles 312 from theEM energy 302 and the EM energy 308, respectively. As non-limitingexamples, the angle-finding module 130 can use a pseudo-spectrumfunction, including a Space-Alternating GeneralizedExpectation-maximization (SAGE), Delay-and-Sum (DS), Minimum VarianceDistortionless Response (MVDR), and/or a Multiple Signal Classification(MUSIC) based-function, to calculate the direction of arrival of the EMsignals received by the azimuth subarray 206 and the elevation subarray208. As another example, the angle-finding module can use an Estimationof Signal Parameters via Rotational Invariance Technique (ESPRIT)technique or FFT beamforming to calculate the azimuth angles 306 and theelevation angles 312. The angle-finding module 130 can determine theazimuth angles 306 and the elevation angles 312 with relatively lowprocessing complexity and cost.

At 316, the angle-finding module 130 associates, using EM energy 314received by the 2D subarray 208, the azimuth angles 306 and theelevation angles 312 to the objects 106. In particular, theangle-finding module 130 determines the azimuth angle 306 and theelevation angle 312 associated with each of the one or more objects 106.The association of the azimuth angles 306 to the elevation angles 312 isdescribed in greater detail with respect to FIG. 4 .

FIG. 4 illustrates an example flow diagram 316 of the angle-findingmodule 130 to associate the azimuth angles 306 and the elevation angles312 to respective objects 106. The angle-finding module 130 of FIG. 4can, for example, be the angle-finding module 130 of FIGS. 1-3 . Asdescribed with respect to FIG. 3 , the angle-finding module 130determines the azimuth angles 306 and the elevation angles 312associated with the azimuth objects and the elevation objects,respectively.

At 402, the angle-finding module 130 can define a coordinate system forthe antenna elements 210 of the 2D subarray 208. For example, theangle-finding module 130 can denote the coordinate of the mostbottom-left antenna element 210 of the 2D subarray 208 in antenna 200-1as (0, 0). The coordinates of the other antenna elements 210 in the 2Dsubarray 208 can be denoted as

(d_(AZ)⁽¹⁾, d_(EL)⁽¹⁾), (d_(AZ)⁽²⁾, d_(EL)⁽²⁾), …  , (d_(AZ)^((K − 1)), d_(EL)^((K − 1))),where K represents the total number of antenna elements 210 in the 2Dsubarray and d_(AZ) ^((i-1)) and d_(EL) ^((i-1)) represents the azimuthdistance 212 and the elevation distance 214 from the ith antenna element210 to the most bottom-left antenna element 210, respectively.

At 404, the angle-finding module 130 can generate, using the coordinatesystem, a dictionary matrix 406 of steering vectors that include each ofthe azimuth angles 306 paired with each of the elevation angles 312. Ifa pair of an azimuth angle 306 and an elevation angle 312 of a pointscatterer is given as (θ, φ), the angle-finding module 130 can generatea K×1 steering vector:α(θ,φ)=[1,e ^(−j2π(d) ^(az) ⁽¹⁾ ^(sin θ+d) ^(el) ⁽¹⁾ ^(sin φ)/λ) ,e^(−j2π(d) ^(az) ⁽²⁾ ^(sin θ+d) ^(el) ⁽²⁾ ^(sin φ)/λ) , . . . ,e^(−j2π(d) ^(az) ^((K-1)) ^(sin θ+d) ^(el) ^((K-1)) ^(sin φ)/λ)]^(T)  (1)where λ represents the wavelength of the EM signal transmitted andreceived by the radar system 102.

The angle-finding module 130 can use the azimuth angles 306, θ₁, θ₂, . .. , θ_(N) _(AZ) , and the elevation angles 312, φ₁, φ₂, . . . , φ_(N)_(EL) , to form N_(AZ)N_(EL) angle pairs. The angles of the objects 106are included within the N_(AZ)N_(EL) angle pairs.

For each angle pair (θ_(u), φ_(v)), where u∈{1, 2, . . . , N_(AZ)} andv∈{1, 2, . . . , N_(EL)}, the angle-finding module 130 can define asteering vector for the 2D subarray 208 as:α(θ_(u),φ_(v))=[1,e ^(−j2π(d) ^(AZ) ⁽¹⁾ ^(sin θ) ^(u) ^(+d) ^(EL) ⁽¹⁾^(sin φ) ^(v) ^()/λ) , . . . ,e ^(−j2π(d) ^(AZ) ^((K-1)) ^(sin θ) ^(u)^(+d) ^(EL) ^((K-1)) ^(sin φ) ^(v) ^()/λ)]^(T)  (2)

The angle-finding module 130 can assemble the steering vectors for theangle pairs into the K×N_(AZ)N_(EL) dictionary matrix 406:

$\begin{matrix}{A = \lbrack {{a( {\theta_{u_{1}},\varphi_{v_{1}}} )},{a( {\theta_{u_{2}},\varphi_{v_{2}}} )},\ldots\mspace{14mu},{a( {\theta_{u_{N_{AZ}N_{EL}}},\varphi_{v_{N_{AZ}N_{EL}}}} )}} \rbrack} & (3)\end{matrix}$

At 408, the angle-finding module 130 can determine, using anL1-minimization based-function and the EM energy 314 received by the 2Dsubarray 208, non-zero elements in a selection vector. The non-zeroelements in the selection vector represent actual angle pairs 410 of thedictionary matrix 406 that correspond to the azimuth angle 306 and theelevation angle 312 of the respective objects 106.

Because the actual pairs 410 of the objects 106 should be within theN_(AZ)N_(EL) angle pairs, the angle-finding module 130 can use thefollowing equation to identify the actual pairs 410:y=Ax+η  (4)where the K×1 vector y represents the measured beam vector of the EMenergy 314 received by the 2D subarray 208, the N_(AZ)N_(EL)×1 vector xrepresents a parse vector, and the K×1 vector η represents measurementnoise. The angle-finding module 130 considers x as the selection vector.The steering vectors in A corresponding to the non-zero elements in xrepresent the actual pairs 410.

The angle-finding module 130 can solve for the x in Equation (4) bysolving the following L1-minimization:

$\begin{matrix}{{\hat{x} = {\arg{\min\limits_{x}{x}_{1}}}},{{s.t.\mspace{14mu}{{y - {Ax}}}_{2}} \leq ɛ}} & (5)\end{matrix}$where ε bounds the amount of noise in the data. The angle-finding module130 can solve Equation (5) using, for example, an Orthogonal MatchingPursuit (OMP) based-function.

Example Method

FIG. 5 illustrates an example method 500 of the radar system 102 withmodified orthogonal linear antenna subarrays and the angle-findingmodule 130. Method 500 is shown as sets of operations (or acts)performed, but not necessarily limited to the order or combinations inwhich the operations are shown herein. Further, any of one or more ofthe operations may be repeated, combined, or reorganized to provideother methods. In portions of the following discussion, reference may bemade to the environment 100 of FIG. 1 , and entities detailed in FIGS. 1through 4 , reference to which is made for example only. The techniquesare not limited to performance by one entity or multiple entities.

At 502, an antenna of a radar system receives EM energy reflected by oneor more objects. For example, the antenna 200 of the radar system 102can receive EM energy reflected by the one or more objects 106.

At 504, first angles associated with one or more first objects aredetermined using EM energy received by a first 1D subarray of theantenna. The one or more first objects are a first subset of the one ormore objects. For example, the processor 126 of the radar system 102 candetermine, using the angle-finding module 130 and the EM energy 302received by the azimuth subarray 204, the azimuth angles 306 associatedwith one or more azimuth objects. The one or more azimuth objects are afirst subset of the one or more objects 106.

At 506, second angles associated with one or more second objects aredetermined using EM energy received by a second 1D subarray of theantenna. The one or more second objects are a second subset of the oneor more objects. The second 1D subarray is positioned orthogonal to thefirst 1D subarray. For example, the processor 126 can determine, usingthe angle-finding module 130 and the EM energy 308 received by theelevation subarray 206, the elevation angles 312 associated with one ormore elevation objects. The one or more elevation objects are a secondsubset of the one or more objects 106. The elevation subarray 206 ispositioned orthogonal to the azimuth subarray 204.

At 508, the first angles and the second angles are associated withrespective objects of the one or more objects using EM energy receivedby a 2D subarray. The 2D subarray includes at least four antennaelements not encompassed by the first 1D subarray or the second 1Dsubarray. For example, the processor 126 can associate, using theangle-finding module 130 and the EM energy 314 received by the 2Dsubarray 208, the azimuth angles 306 and the elevation angles 312 withrespective objects of the one or more objects 106. The 2D subarray 208includes at least four antenna elements 210 that are not encompassed bythe azimuth subarray 204 and the elevation subarray 206.

EXAMPLES

In the following section, examples are provided.

Example 1: A radar system comprising: an antenna configured to receiveelectromagnetic (EM) energy reflected by one or more objects, theantenna comprising: a first one-dimensional subarray; a secondone-dimensional subarray positioned orthogonal to the firstone-dimensional subarray; and a two-dimensional subarray comprising atleast four antenna elements not encompassed by the first one-dimensionalsubarray or the second one-dimensional subarray; and one or moreprocessors configured to: determine, using the EM energy received by thefirst one-dimensional subarray, first angles associated with one or morefirst objects, the one or more first objects comprising a first subsetof the one or more objects; determine, using the EM energy received bythe second one-dimensional subarray, second angles associated with oneor more second objects, the one or more second objects comprising asecond subset of the one or more objects; and associate, using the EMenergy received by the two-dimensional subarray, the first angles andthe second angles with respective objects of the one or more objects.

Example 2: The radar system of example 1, wherein the one or moreprocessors are configured to associate the first angles and the secondangles with the respective objects of the one or more objects in thefollowing manner: define a coordinate system for the antenna elements ofthe two-dimensional subarray; generate, using the coordinate system, adictionary matrix of steering vectors that include each of the firstangles paired with each of the second angles; and determine, using anL1-minimization based-function and the EM energy received by thetwo-dimensional subarray, non-zero elements in a selection vector, thenon-zero elements in the selection vector representing pairs of thefirst angle and the second angle in the dictionary matrix thatcorrespond to the first angles and the second angles of the respectiveobjects of the one or more objects.

Example 3: The radar system of example 1, wherein the firstone-dimensional subarray is positioned in an azimuth direction and thesecond one-dimensional subarray is positioned in an elevation direction.

Example 4: The radar system of example 1, wherein the firstone-dimensional subarray and the second one-dimensional subarray arelinear subarrays.

Example 5: The radar system of example 4, wherein the firstone-dimensional subarray and the second one-dimensional subarray areconfigured in an approximately L-shape, an approximately T-shape, or anapproximately cross shape.

Example 6: The radar system of example 1, wherein the firstone-dimensional subarray comprises a first number of antenna elementsand the second one-dimensional subarray comprises a second number ofantenna elements, the first number of antenna elements not equal to thesecond number of antenna elements.

Example 7: The radar system of example 6, wherein the two-dimensionalsubarray comprises a third number of antenna elements, the third numberof antenna elements is less than a half of a product of the first numberof antenna elements and the second number of antenna elements.

Example 8: The radar system of example 1, wherein the antenna elementsof the two-dimensional subarray are configured in an approximatelyrectangular shape.

Example 9: The radar system of example 1, wherein the antenna elementsof the two-dimensional subarray are positioned in a sparse array.

Example 10: The radar system of example 1, wherein the number of antennaelements in the two-dimensional subarray is greater than an anticipatedmaximum number of objects of the radar system.

Example 11: The radar system of example 1, wherein the antenna elementsof the two-dimensional subarray are not included in the firstone-dimensional subarray or the second one-dimensional subarray.

Example 12: The radar system of example 1, wherein the first angles andthe second angles are determined using at least one of an Estimation ofSignal Parameters via Rotational Invariance Technique (ESPRIT),Space-Alternating Generalized Expectation-maximization (SAGE),Delay-and-Sum (DS), Minimum Variance Distortionless Response (MVDR), aMultiple Signal Classification (MUSIC), or a fast Fourier transform(FFT) beamforming based-function.

Example 13: The radar system of example 1, wherein the radar system isconfigured to be installed on an automobile.

Example 14: A method comprising: receiving, by an antenna of a radarsystem, electromagnetic (EM) energy reflected by one or more objects;determining, using the EM energy received by a first one-dimensionalsubarray of the antenna, first angles associated with one or more firstobjects, the one or more first objects comprising a first subset of theone or more objects; determining, using the EM energy received by asecond one-dimensional subarray of the antenna, second angles associatedwith one or more second objects, the one or more second objectscomprising a second subset of the one or more objects, the secondone-dimensional subarray positioned orthogonal to the firstone-dimensional subarray; and associating, using the EM energy receivedby a two-dimensional subarray, the first angles and the second angleswith respective objects of the one or more objects, the two-dimensionalsubarray comprising at least four antenna elements not encompassed bythe first one-dimensional subarray or the second one-dimensionalsubarray.

Example 15: The method of example 14, wherein associating the firstangles and the second angles with the respective objects of the one ormore objects comprises: defining a coordinate system for the antennaelements of the two-dimensional subarray; generating, using thecoordinate system, a dictionary matrix of steering vectors that includeeach of the first angles paired with each of the second angles; anddetermining, using an L1-minimization based-function and the EM energyreceived by the two-dimensional subarray, non-zero elements in aselection vector, the non-zero elements in the selection vectorrepresenting pairs of the first angle and the second angle in thedictionary matrix that correspond to the first angles and the secondangles of the respective objects of the one or more objects.

Example 16: The method of example 14, wherein the first one-dimensionalsubarray is positioned in an azimuth direction, and the secondone-dimensional subarray is positioned in an elevation direction.

Example 17: The method of example 14, the antenna elements of thetwo-dimensional subarray are positioned in a sparse array.

Example 18: A computer-readable storage media comprisingcomputer-executable instructions that, when executed, cause a processorof a radar system to: receive, by an antenna of the radar system,electromagnetic (EM) energy reflected by one or more objects; determine,using the EM energy received by a first one-dimensional subarray of theantenna, first angles associated with one or more first objects, the oneor more first objects comprising a first subset of the one or moreobjects; determine, using the EM energy received by a secondone-dimensional subarray of the antenna, second angles associated withone or more second objects, the one or more second objects comprising asecond subset of the one or more objects, the second one-dimensionalsubarray positioned orthogonal to the first one-dimensional subarray;and associate, using the EM energy received by a two-dimensionalsubarray, the first angles and the second angles with respective objectsof the one or more objects, the two-dimensional subarray comprising atleast four antenna elements not encompassed by the first one-dimensionalsubarray or the second one-dimensional subarray.

Example 19: The computer-readable storage media of example 18, whereinthe computer-executable instructions, to associate the first angles andthe second angles with the respective objects, cause the processor ofthe radar system to: define a coordinate system for the antenna elementsof the two-dimensional subarray; generate, using the coordinate system,a dictionary matrix of steering vectors that include each of the firstangles paired with each of the second angles; and determine, using anL1-minimization based-function and the EM energy received by thetwo-dimensional subarray, non-zero elements in a selection vector, thenon-zero elements in the selection vector representing pairs of thefirst angle and the second angle in the dictionary matrix thatcorrespond to the first angles and the second angles of the respectiveobjects of the one or more objects.

Example 20: The computer-readable storage media of example 18, whereinthe first one-dimensional subarray is positioned in an azimuth directionand the second one-dimensional subarray is positioned in an elevationdirection.

CONCLUSION

While various embodiments of the disclosure are described in theforegoing description and shown in the drawings, it is to be understoodthat this disclosure is not limited thereto but may be variouslyembodied to practice within the scope of the following claims. From theforegoing description, it will be apparent that various changes may bemade without departing from the spirit and scope of the disclosure asdefined by the following claims.

What is claimed is:
 1. A radar system comprising: an antenna configuredto receive electromagnetic (EM) energy reflected by one or more objects,the antenna comprising: a first one-dimensional subarray comprising afirst number of antenna elements; a second one-dimensional subarraypositioned orthogonal to the first one-dimensional subarray andcomprising a second number of antenna elements; and a two-dimensionalsubarray comprising at least four antenna elements not encompassed bythe first one-dimensional subarray or the second one-dimensionalsubarray, the two-dimensional subarray comprising a third number ofantenna elements, the third number of antenna elements being less than aproduct of the first number of antenna elements and the second number ofantenna elements; and one or more processors configured to: determine,using the EM energy received by the first one-dimensional subarray,first angles associated with one or more first objects, the one or morefirst objects comprising a first subset of the one or more objects;determine, using the EM energy received by the second one-dimensionalsubarray, second angles associated with one or more second objects, thesecond angles being orthogonal to the first angles, the one or moresecond objects comprising a second subset of the one or more objects;and associate, using the EM energy received by the two-dimensionalsubarray, the first angles and the second angles with respective objectsof the one or more objects.
 2. The radar system of claim 1, wherein theone or more processors are configured to associate the first angles andthe second angles with the respective objects of the one or more objectsby: defining a coordinate system for the antenna elements of thetwo-dimensional subarray; generating, using the coordinate system, adictionary matrix of steering vectors that include each of the firstangles paired with each of the second angles; and determining, using anL1-minimization based-function and the EM energy received by thetwo-dimensional subarray, non-zero elements in a selection vector, thenon-zero elements in the selection vector representing pairs of thefirst angle and the second angle in the dictionary matrix thatcorrespond to the first angles and the second angles of the respectiveobjects of the one or more objects.
 3. The radar system of claim 1,wherein the first one-dimensional subarray is positioned in an azimuthdirection and the second one-dimensional subarray is positioned in anelevation direction.
 4. The radar system of claim 1, wherein the firstone-dimensional subarray and the second one-dimensional subarray arelinear subarrays.
 5. The radar system of claim 4, wherein the firstone-dimensional subarray and the second one-dimensional subarray areconfigured in an approximately L-shape, an approximately T-shape, or anapproximately cross shape.
 6. The radar system of claim 1, wherein thefirst number of antenna elements is not equal to the second number ofantenna elements.
 7. The radar system of claim 1, wherein the thirdnumber of antenna elements is less than a half of the product of thefirst number of antenna elements and the second number of antennaelements.
 8. The radar system of claim 1, wherein the antenna elementsof the two-dimensional subarray are configured in an approximatelyrectangular shape.
 9. The radar system of claim 1, wherein the antennaelements of the two-dimensional subarray are positioned in a sparsearray.
 10. The radar system of claim 1, wherein the number of antennaelements in the two-dimensional subarray is greater than an anticipatedmaximum number of objects of the radar system.
 11. The radar system ofclaim 1, wherein the antenna elements of the two-dimensional subarrayare not included in the first one-dimensional subarray or the secondone-dimensional subarray.
 12. The radar system of claim 1, wherein thefirst angles and the second angles are determined using at least one ofan Estimation of Signal Parameters via Rotational Invariance Technique(ESPRIT), Space-Alternating Generalized Expectation-maximization (SAGE),Delay-and-Sum (DS), Minimum Variance Distortionless Response (MVDR), aMultiple Signal Classification (MUSIC), or a fast Fourier transform(FFT) beamforming based-function.
 13. The radar system of claim 1,wherein the radar system is configured to be installed on an automobile.14. A method comprising: receiving, by an antenna of a radar system,electromagnetic (EM) energy reflected by one or more objects;determining, using the EM energy received by a first one-dimensionalsubarray of the antenna, first angles associated with one or more firstobjects, the one or more first objects comprising a first subset of theone or more objects, the first one-dimensional subarray comprising afirst number of antenna elements; determining, using the EM energyreceived by a second one-dimensional subarray of the antenna, secondangles associated with one or more second objects, the second anglesbeing orthogonal to the first angles, the one or more second objectscomprising a second subset of the one or more objects, the secondone-dimensional subarray positioned orthogonal to the firstone-dimensional subarray and comprising a second number of antennaelements; and associating, using the EM energy received by atwo-dimensional subarray, the first angles and the second angles withrespective objects of the one or more objects, the two-dimensionalsubarray comprising at least four antenna elements not encompassed bythe first one-dimensional subarray or the second one-dimensionalsubarray, the two-dimensional subarray comprising a third number ofantenna elements, the third number of antenna elements being less than aproduct of the first number of antenna elements and the second number ofantenna elements.
 15. The method of claim 14, wherein associating thefirst angles and the second angles with the respective objects of theone or more objects comprises: defining a coordinate system for theantenna elements of the two-dimensional subarray; generating, using thecoordinate system, a dictionary matrix of steering vectors that includeeach of the first angles paired with each of the second angles; anddetermining, using an L1-minimization based-function and the EM energyreceived by the two-dimensional subarray, non-zero elements in aselection vector, the non-zero elements in the selection vectorrepresenting pairs of the first angle and the second angle in thedictionary matrix that correspond to the first angles and the secondangles of the respective objects of the one or more objects.
 16. Themethod of claim 14, wherein the first one-dimensional subarray ispositioned in an azimuth direction and the second one-dimensionalsubarray is positioned in an elevation direction.
 17. The method ofclaim 14, wherein the antenna elements of the two-dimensional subarrayare positioned in a sparse array.
 18. Non-transitory computer-readablestorage media comprising computer-executable instructions that, whenexecuted, cause a processor of a radar system to: receive, by an antennaof the radar system, electromagnetic (EM) energy reflected by one ormore objects; determine, using the EM energy received by a firstone-dimensional subarray of the antenna, first angles associated withone or more first objects, the one or more first objects comprising afirst subset of the one or more objects, the first one-dimensionalsubarray comprising a first number of antenna elements; determine, usingthe EM energy received by a second one-dimensional subarray of theantenna, second angles associated with one or more second objects, thesecond angles being orthogonal to the first angles, the one or moresecond objects comprising a second subset of the one or more objects,the second one-dimensional subarray positioned orthogonal to the firstone-dimensional subarray and comprising a second number of antennaelements; and associate, using the EM energy received by atwo-dimensional subarray, the first angles and the second angles withrespective objects of the one or more objects, the two-dimensionalsubarray comprising at least four antenna elements not encompassed bythe first one-dimensional subarray or the second one-dimensionalsubarray, the two-dimensional subarray comprising a third number ofantenna elements, the third number of antenna elements being less than aproduct of the first number of antenna elements and the second number ofantenna elements.
 19. The non-transitory computer-readable storage mediaof claim 18, wherein the computer-executable instructions, to associatethe first angles and the second angles with the respective objects,cause the processor of the radar system to: define a coordinate systemfor the antenna elements of the two-dimensional subarray; generate,using the coordinate system, a dictionary matrix of steering vectorsthat include each of the first angles paired with each of the secondangles; and determine, using an L1-minimization based-function and theEM energy received by the two-dimensional subarray, non-zero elements ina selection vector, the non-zero elements in the selection vectorrepresenting pairs of the first angle and the second angle in thedictionary matrix that correspond to the first angles and the secondangles of the respective objects of the one or more objects.
 20. Thenon-transitory computer-readable storage media of claim 18, wherein thefirst one-dimensional subarray is positioned in an azimuth direction andthe second one-dimensional subarray is positioned in an elevationdirection.